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 共查询到19条相似文献,搜索用时 78 毫秒
1.
建立了无限区间上的积一微分方程的比较定理,用上下解方法证明了无限区间上的Banach空间积-微分方程的初值问题的解的存在性.  相似文献   

2.
建立了无限区间上二阶积-微分方程的比较定理,用上下解方法证明了无限区间上的Ba-nach空间二阶非线性积-微分方程的初值问题的解的存在性.  相似文献   

3.
研究了Sturm-Liouville算子Aq,h,Hj,j=1,2,…中势函数q(x)的确定性问题,即已知部分区间[a,1](a∈(0,1))上的势函数q(x),则无限组部分谱信息可唯一确定整个区间[0,1]上的势函数.推广了Simon的方法,且将选择条件的范围从一组谱扩展到了无限组.  相似文献   

4.
介绍应用微分中值定理时,构造所需辅助函数的两种有效方法:观察法和解微分方程法。并通过变量代换法化无限为有限,将罗尔定理的应用推广到无限区间上。  相似文献   

5.
本文研究一类无限区间上具有Riemann-Liouville 导数的多分数阶非线性微分方程初值问题,在一类加权函数空间上使用Schauder 不动点定理建立了该问题解的存在性和唯一性结果, 举例说明了定理的应用.  相似文献   

6.
对罗尔定理进行深入系统的探讨和研究.给出在更弱条件下的各种区间类型(包括有限区间和无限区间)的罗尔定理的推广形式.  相似文献   

7.
局部保号性是连续函数的一个重要性质,在已有文献基础上进一步讨论函数的局部保号性,给出了导函数在非连续点处的一个局部无限保号性.设f(x)是区间I上的可导函数,f′(x_0)0 (其中x_0∈I,f′(x)在x_0处不必连续),则任给x_0的开邻域■是区间I的无限子集.这一结果进一步深化了函数在非连续点处的局部保号性理论.  相似文献   

8.
讨论一类非线性向量微分方程无穷边值问题的奇摄动,虽然此类边值问题在有限区间上曾被广泛地研究过,但在无限区间上还未曾采用对角化的方法去研究它.在适当的条件下,该文采用新的方法去证明解的存在性和任意阶的一致有效的渐近展开式,同时也给出误差估计.  相似文献   

9.
利用不动点指数理论和Krein-Rutman定理,证明了半无限区间上具有一阶导数的奇异二阶多点边值问题的正解存在性,其中的非线性项可以在任意一点具有奇性和不连续性.该结论扩展了现有的一些结果.  相似文献   

10.
以微分中值定理的几何意义作为切入点,将微分中值定理的适用区间从原来的有限区间[a,b]推广到无限区间(-∞,+∞),并给出相应的推广结论.  相似文献   

11.
The density of polynomials is straightforward to prove in Sobolev spaces Wk,p((a,b)), but there exist only partial results in weighted Sobolev spaces; here we improve some of these theorems. The situation is more complicated in infinite intervals, even for weighted Lp spaces; besides, in the present paper we have proved some other results for weighted Sobolev spaces in infinite intervals.  相似文献   

12.
无穷区间上的二阶边值问题的多解性   总被引:1,自引:0,他引:1  
讨论了无穷区间上的一类二阶两点边值问题,通过运用Leggett-Williams不动点定理,得到了新的三个正解的存在性结果。  相似文献   

13.
研究了一类在无穷区间上具有p-Laplacian算子的边值问题的迭代正解.利用单调迭代方法得到问题的迭代正解存在性的充分条件,同时得到了解的相应迭代序列,最后给出例子证明所得结论.  相似文献   

14.
More general and stronger estimations of bounds for the fundamental functions of Hermite interpolation of high order on an arbitrary system of nodes on infinite intervals are given. Based on this result, convergence of Gaussian quadrature formulas for Riemann–Stieltjes integrable functions on an arbitrary system of nodes on infinite intervals is discussed.  相似文献   

15.
The class of intersection graphs of unit intervals of the real line whose ends may be open or closed is a strict superclass of the well-known class of unit interval graphs. We pose a conjecture concerning characterizations of such mixed unit interval graphs, verify parts of it in general, and prove it completely for diamond-free graphs. In particular, we characterize diamond-free mixed unit interval graphs by means of an infinite family of forbidden induced subgraphs, and we show that a diamond-free graph is mixed unit interval if and only if it has intersection representations using unit intervals such that all ends of the intervals are integral.  相似文献   

16.
In this paper, we consider a fractional impulsive boundary value problem on infinite intervals. We obtain the existence, uniqueness and computational method of unbounded positive solutions.  相似文献   

17.
We revisit the old problem of finding the stability and instability intervals of a second-order elliptic equation on the real line with periodic coefficients (Hill's equation). It is well known that the stability intervals correspond to the spectrum of the Bloch family of operators defined on a single period. Here we propose a characterization of the instability intervals. We introduce a new family of non-self-adjoint operators, formally equivalent to the Bloch ones but with an imaginary Bloch parameter, that we call exponential. We prove that they admit a countable infinite number of eigenvalues which, when they are real, completely characterize the intervals of instability of Hill's equation.  相似文献   

18.
In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the ap- proximation. To improve the approximation rate, we further introduce a type of combinations of neurM networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals.  相似文献   

19.
Adaptive quadrature codes process a collection of subintervals one at a time. We show how to process them all simultaneously and so exploit vectorization and the use of fast built-in functions and array operations that are so important to efficient computation in MATLAB. Using algebraic transformations we have made it just as easy for users to solve problems on infinite intervals and with moderate end point singularities as problems with finite intervals and smooth integrands. Piecewise-smooth integrands are handled effectively with breakpoints.  相似文献   

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